Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

Can you make square numbers by adding two prime numbers together?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Can you work out some different ways to balance this equation?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

An investigation that gives you the opportunity to make and justify predictions.

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Have a go at balancing this equation. Can you find different ways of doing it?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

An environment which simulates working with Cuisenaire rods.

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

How many different sets of numbers with at least four members can you find in the numbers in this box?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

Given the products of adjacent cells, can you complete this Sudoku?

If you have only four weights, where could you place them in order to balance this equaliser?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Got It game for an adult and child. How can you play so that you know you will always win?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Can you complete this jigsaw of the multiplication square?

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?